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how to caculate the Galerkin projection

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Old   March 15, 2006, 08:46
Default how to caculate the Galerkin projection
  #1
ztdep
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hell0:

I don not how to caculate the Galerkin projection.

( laplace(T), phi )

Where phi is the basis, and i want to project the laplace(T) onto the phi, but 1), what is the meaning of ( ) , and i have the value of T only at discrete points, then how to caculate it.

regards!
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Old   March 15, 2006, 09:34
Default Re: how to caculate the Galerkin projection
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al
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Let us assume a(x) and b(x) two functions in an interval [0,1]. Then (a,b)=integral a(x) b(x) dx

means the inner product, (dot product), between the functions a and b. This can be considered as a projection of a() into b() and the other way around.

This is much more simple, for the case of simple vectors, e.g. a=[1 0 1] and b=[1 0 0] (a,b) = |a| |b| cos( angle (a,b) )

Equivalent, (laplace(T),phi) means that you want to determine the projection of laplace(T) into phi.

Why do you have only discrete points? Are you using a Galerkin spectral method?

Any way, if you have only T at some points, e.g. T[i] , then you can compute approximately laplace(T) at the same points, laplace(T)[i]. Then you can approximate the inner product as

(laplace(T),phi)= laplace(T)[1] phi[1] Deltax + laplace(T)[2] phi[2] Deltax+ ...

where Deltax is the space between the points.

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Old   March 15, 2006, 21:36
Default Re: how to caculate the Galerkin projection
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ztdep
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Hi,Wed:

thank you for your feedback!

would you like to give me your email address, i have some question!

regards!

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Old   March 15, 2006, 23:52
Default Re: how to caculate the Galerkin projection
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Mike
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See here

http://community.livejournal.com/res....html#comments

Mike
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Old   March 16, 2006, 01:03
Default Re: how to caculate the Galerkin projection
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ztdep
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Mike:

what have you give me! i can not get any information from it? then how to use it
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Old   March 16, 2006, 01:49
Default Re: how to caculate the Galerkin projection
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Mike
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My name is "Michail" and I'm Russian

in Russian it means "BEAR"

http://community.livejournal.com/ru_preved/

Bear is our natianal HERO

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